The EA has also warned people to avoid walking or driving through floodwater.
In Gargrave, rescue crews said several properties “on the same street” had their basements flooded, with crews called out at about 08:45 GMT on Wednesday morning.
The fire service was also called to help multiple drivers left stranded in floodwater throughout the day, including in Northallerton, Ripon and Hawes.
Rescue crews said they had winched a vehicle, which was in danger of being swept out into the Ouse, to a “safe place”.
Besides York, flood warnings in North Yorkshire are also in place at Boroughbridge, Masham, Naburn, Cowthorpe, near Wetherby, and Newsham, near Thirsk.
In West Yorkshire, Allerton Bywater near Castleford, Horbury in Wakefield and part of Bingley are also covered by warnings.
A further 24 orange flood alerts, which indicate flooding is possible, also remained in place across the whole of Yorkshire, as of 18:15.
In East Yorkshire, the Priory Road area of Hull was one of the places covered by an alert.